In terms of the second question, it is difficult to ascertain the level of privacy gained by creating a synthetic data set. If a method is used which employs \(\epsilon -\) differential privacy, then the privacy budget, \(\epsilon \) , can be used as a metric for how well the data is protected, however it is not always practical to use \(\epsilon -\) differential privacy methods when working with image generation.
Indeed, it was noted in [1]} that generators trained in such a differentially-private way fail to maintain a trade-off between sample quality and
diversity. It has been shown in recent work that under some assumptions, synthetic data samples generated using GANs are inherently \((\epsilon , \delta )-\)  differentially private [2]}.
